锥广义类凸集值映射的择一性定理及应用  

Theorem of Alternative for Cone Generalized Convexlike Set-valued Maps and It's Applications

作　　者：施绍萍[1] 揭志勇 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]南昌陆军学院科文教研室,江西南昌330103

出　　处：《南昌大学学报（理科版）》2010年第6期520-522,共3页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(2009GZS0021)

摘　　要：将单值映射的锥广义类凸概念拓广到集值映射,引入了集值映射的锥广义类凸性,然后建立了一个择一性定理,并借助它导出了锥广义类凸集值映射优化问题的标量化结果和Lagrange乘子定理。By extending the concept of cone generalized convexlikeness of single-valued maps,it first introduce cone generalized convexlikeness of set-valued maps,and then give a theorem of the alternative.Furthermore,scalarization result and Lagrange multiplier theorem are established by using the alternative theorem.

关 键 词：集值映射 锥广义类凸性 择一定理 标量化 LAGRANGE乘子定理 

分 类 号：O221[理学—运筹学与控制论]